Finite Group Databasebeta

← #14922676

Subgroups — #14922676

Order 2816.

2662 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623199C211yesmaximal, characteristic
2C2×C4×#4343C211yesmaximal, characteristic, complemented
3#13072410C211yesmaximal, characteristic, complemented
4#13072405C211yesmaximal, characteristic, complemented
5#13072403C211yesmaximal, characteristic, complemented
6#13072390C211yesmaximal, characteristic, complemented
7#13072386C211yesmaximal, characteristic, complemented
8#13072384C211yesmaximal, characteristic, complemented
9#13072382C211yesmaximal, characteristic, complemented
10#13072373C212yesmaximal, complemented
11#13072369C212yesmaximal, complemented
12#13072358C212yesmaximal, complemented
13#13072354C212yesmaximal, complemented
14#13071881C212yesmaximal, complemented
15#13071878C212yesmaximal, complemented
16#13071143C212yesmaximal, complemented
17#13071143C212yesmaximal, complemented
18#13071105C211yesmaximal, characteristic, complemented
19#13071103C211yesmaximal, characteristic, complemented
20#13071103C211yesmaximal, characteristic, complemented
21#13071097C211yesmaximal, characteristic, complemented
22C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2448C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C22×#4341C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×#66997C2211yescharacteristic
30C2×#66993C2211yescharacteristic
31#10623199—28no—
32C4×#4343—28no—
33C2×#66946C2211yescharacteristic
34C2×#66946C2212yes—
35C2×#66945C2211yescharacteristic
36C2×#66945C2212yes—
37C2×#66945C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66937C2212yes—
41C2×#66937C2212yes—
42C2×#66936C2212yes—
43C2×#66936C2212yes—
44C2×(C22⋊D11)⋊C4C2212yes—
45C2×(C22⋊D11)⋊C4C2212yes—
46C2×#66928C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48C2×C4×D44C2212yes—
49C2×C42×D11C2211yescharacteristic
50C2×C42×D11C2212yes—
51C2×C42×D11C2211yescharacteristic
52C2×C42×D11C2211yescharacteristic
53C11×#399C2212yes—
54C11×#397C2212yes—
55C11×#391C2211yescharacteristic
56C11×#390C2211yescharacteristic
57C11×#390C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#388C2212yes—
60C11×#388C2212yes—
61C4×C11×C4⋊C4C2211yescharacteristic
62#10622843C2211yescharacteristic
63#10622834C2211yescharacteristic
64#10622834C2211yescharacteristic
65#10622606C2212yes—
66#10622606C2212yes—
67#10622602C2212yes—
68#10622602C2212yes—
69#10622602C2212yes—
70#10622601C2211yescharacteristic
71#10622598C2211yescharacteristic
72#10622595C2212yes—
73#10622593C2212yes—
74C4⋊C4×Dic11C2211yescharacteristic
75C4⋊C4×Dic11C2212yes—
76C4⋊C4×Dic11C2211yescharacteristic
77#10622587C2211yescharacteristic
78#10622587C2211yescharacteristic
79#10622586C2211yescharacteristic
80#10622574C2212yes—
81#10622574C2212yes—
82#10622572C2212yes—
83#10622572C2212yes—
84#10622569C2212yes—
85#10622569C2212yes—
86#10622569C2212yes—
87#10622569C2212yes—
88#10622569C2212yes—
89#10622569C2212yes—
90#10622566C2212yes—
91#10622562C2212yes—
92#10622557C2212yes—
93#10622557C2212yes—
94C22⋊C4×Dic11C2212yes—
95C22⋊C4×Dic11C2212yes—
96C22⋊C4×Dic11C2212yes—
97C22⋊C4×Dic11C2212yes—
98#10622552C2211yescharacteristic
99C4×C4⋊Dic11C2211yescharacteristic
100#10622546C2212yes—
101#10622546C2212yes—
102C4×Dic11⋊C4C2211yescharacteristic
103C4×Dic11⋊C4C2211yescharacteristic
104#10622542C2211yescharacteristic
105#10622542C2211yescharacteristic
106#10622541C2211yescharacteristic
107#10622288C2212yes—
108#10622288C2212yes—
109#10622281C2212yes—
110#10622279C2212yes—
111#10622279C2212yes—
112#10622278C2212yes—
113#10622278C2212yes—
114#10622277C2212yes—
115#10622277C2212yes—
116D11×#95C2211yescharacteristic
117D11×#95C2211yescharacteristic
118#10622274C2212yes—
119#10622272C2212yes—
120#10622266C2212yes—
121#10622266C2212yes—
122#10622262C2211yescharacteristic
123#10622262C2212yes—
124#10622262C2211yescharacteristic
125C22×Q8×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2312yes—
129C22×C22⋊D11C2312yes—
130C23×Dic11C2312yes—
131C2×#4343—24no—
132C2×#4343—24no—
133C2×#4343D418yes—
134C2×#4341—24no—
135C2×#4341—24no—
136C2×#4341—24no—
137C22×D44C2311yescharacteristic
138C22×D44C2312yes—
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2312yes—
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2312yes—
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2311yescharacteristic
150C11×#124—24no—
151C4×Q8×C11—24no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172Q8×Dic11—24no—
173#66997—24no—
174#66993—24no—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×C4⋊Dic11C2312yes—
186C2×C4⋊Dic11C2311yescharacteristic
187C2×C4⋊Dic11C2312yes—
188C2×C4⋊Dic11C2311yescharacteristic
189C2×C4⋊Dic11C2311yescharacteristic
190C2×C4⋊Dic11C2311yescharacteristic
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2311yescharacteristic
195C2×Dic11⋊C4C2311yescharacteristic
196C2×Dic11⋊C4C2311yescharacteristic
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211#66946—24no—
212#66946—28no—
213#66945—28no—
214#66945—24no—
215#66945—24no—
216C4⋊C4×D11—24no—
217C4⋊C4×D11—24no—
218#66937—28no—
219#66937—28no—
220#66936—28no—
221#66936—28no—
222(C22⋊D11)⋊C4—28no—
223(C22⋊D11)⋊C4—28no—
224#66928—24no—
225C4×D44—24no—
226C4×D44—28no—
227C42×D11—28no—
228C42×D11—24no—
229C42×D11—24no—
230C42×D11—24no—
231C11×#95C2311yescharacteristic
232C11×#95C2311yescharacteristic
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255#34744—111nomaximal, Sylow
256C24×C11C2412yes—
257C23×D11C2412yes—
258C23×D11C2411yescharacteristic
259C2×Q8×C11—22no—
260C2×Q8×C11—22no—
261C2×Q8×C11C2×D414yes—
262C2×D4×C11—22no—
263C2×D4×C11—22no—
264C2×D4×C11—22no—
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2412yes—
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2412yes—
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C22×C4×C11C2412yes—
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C2×C22⋊D11—24no—
276C2×C22⋊D11—24no—
277C2×C22⋊D11—24no—
278C2×C22⋊D11—24no—
279C2×C22⋊D11—24no—
280C2×C22⋊D11—24no—
281C2×C22⋊D11—24no—
282C2×C22⋊D11—42no—
283C2×C22⋊D11—42no—
284C22×Dic11—24no—
285C22×Dic11—24no—
286C22×Dic11—24no—
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2412yes—
292C22×Dic11C2411yescharacteristic
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2411yescharacteristic
297#4343—232no—
298#4341—416no—
299C2×D44—24no—
300C2×D44—24no—
301C2×D44—22no—
302C2×D44—22no—
303C2×D44C2×D414yes—
304C2×D44C2×D418yes—
305C2×C4×D11—22no—
306C2×C4×D11—24no—
307C2×C4×D11—24no—
308C2×C4×D11—24no—
309C2×C4×D11—22no—
310C2×C4×D11—22no—
311C2×C4×D11—22no—
312C2×C4×D11—24no—
313C2×C4×D11—22no—
314C2×C4×D11—22no—
315C2×C4×D11—22no—
316C2×C4×D11—24no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—24no—
322C2×C4×D11—22no—
323C2×C4×D11—41no—
324C2×C4×D11—42no—
325C2×C4×D11—41no—
326C2×C4×D11—41no—
327C2×C4×D11—41no—
328C2×C4×D11—41no—
329C2×C4×D11—42no—
330C2×C4×D11—41no—
331C2×C4×D11C2×D418yes—
332C2×C4×D11C2×D414yes—
333C2×C4×D11#4114yes—
334C2×C4×D11#4114yes—
335C2×Dic22—22no—
336C2×Dic22—22no—
337C2×Dic22—22no—
338C11×C4⋊C4—24no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—22no—
341C11×C4⋊C4—22no—
342C11×C4⋊C4—22no—
343C11×C4⋊C4—42no—
344C11×C22⋊C4—24no—
345C11×C22⋊C4—24no—
346C11×C22⋊C4—24no—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—42no—
349C11×C22⋊C4—42no—
350C42×C11—24no—
351C42×C11—22no—
352C42×C11—22no—
353C42×C11—22no—
354C22⋊Dic11—24no—
355C22⋊Dic11—24no—
356C22⋊Dic11—42no—
357C22⋊Dic11—42no—
358(C2×D11)⋊C4—24no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—24no—
361(C2×D11)⋊C4—24no—
362(C2×D11)⋊C4—24no—
363(C2×D11)⋊C4—24no—
364(C2×D11)⋊C4—24no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368C4⋊Dic11—24no—
369C4⋊Dic11—22no—
370C4⋊Dic11—24no—
371C4⋊Dic11—22no—
372C4⋊Dic11—22no—
373C4⋊Dic11#4114yescomplemented
374Dic11⋊C4—24no—
375Dic11⋊C4—22no—
376Dic11⋊C4—22no—
377Dic11⋊C4—22no—
378Dic11⋊C4—24no—
379Dic11⋊C4—24no—
380Dic11⋊C4—42no—
381Dic11⋊C4#4114yescomplemented
382C4×Dic11—22no—
383C4×Dic11—22no—
384C4×Dic11—22no—
385C4×Dic11—24no—
386C4×Dic11—22no—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—24no—
390C4×Dic11—24no—
391C4×Dic11—22no—
392C4×Dic11—22no—
393C4×Dic11—22no—
394C2×#532—111no—
395C2×C4×#41—111no—
396#2448—111no—
397#2448D1111yescharacteristic, complemented
398#2447—111no—
399#2447—111no—
400#2446—111no—
401#2446—111no—
402#2445—111no—
403#2445—111no—
404#2444—112no—
405#2444—112no—
406#2443—112no—
407#2443—112no—
408#2395—112no—
409#2395—112no—
410C4×#123—112no—
411C4×#123—112no—
412#2297—111no—
413#2297—111no—
414#2297—111no—
415#2296—111no—
416C2×C4×C4⋊C4—111no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11C2511yescharacteristic
425C22×D11—21no—
426C22×D11—21no—
427C22×D11—21no—
428C22×D11—21no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11C22×D414yes—
436C22×D11C22×D412yes—
437C22×D11C2×#4112yes—
438C22×D11C2×#4112yes—
439Q8×C11—28no—
440D4×C11—44no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—22no—
450C2×C4×C11—21no—
451C2×C4×C11—22no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—22no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—22no—
464C2×C4×C11—21no—
465C2×C4×C11C22×D414yes—
466C2×C4×C11C22×D412yes—
467C2×C4×C11C2×#4112yes—
468C2×C4×C11C2×#4112yes—
469C2×C4×C11C2×#4112yes—
470C2×C4×C11C2×#4112yes—
471C22⋊D11—48no—
472C22⋊D11—48no—
473C22⋊D11—48no—
474C2×Dic11—21no—
475C2×Dic11—21no—
476C2×Dic11—21no—
477C2×Dic11—21no—
478C2×Dic11—21no—
479C2×Dic11—21no—
480C2×Dic11—21no—
481C2×Dic11—21no—
482C2×Dic11—21no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—21no—
486C2×Dic11—22no—
487C2×Dic11—21no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—48no—
498C2×Dic11C22×D412yes—
499C2×Dic11C2×#4112yes—
500C2×Dic11C2×#4112yes—
501C2×Dic11C2×#4112yes—
502C2×Dic11C2×#4112yes—
503C2×Dic11C2×#4112yes—
504C2×Dic11C2×#4112yes—
505D44—216no—
506D44—28no—
507C4×D11—28no—
508C4×D11—216no—
509C4×D11—44no—
510C4×D11—48no—
511C4×D11—44no—
512C4×D11—44no—
513C4×D11—44no—
514C4×D11—48no—
515C4×D11—44no—
516C4×D11#123116yescomplemented
517Dic22—44no—
518C22×#41—111no—
519C22×#41—111no—
520#532—228no—
521C2×C4⋊Q8—111no—
522C2×#127—111no—
523C2×#124—111no—
524C2×#124C2×D1111yescharacteristic
525C2×#123—112no—
526C2×#123—112no—
527C2×#121—112no—
528C2×#121—112no—
529C4×#41—228no—
530C2×C4×Q8—111no—
531C2×C4×Q8C2×D1111yescharacteristic
532C2×C4×D4—112no—
533C2×C4×D4—111no—
534C2×C4×D4—112no—
535C2×C4×D4—112no—
536C2×C4×D4—112no—
537C2×C4×D4—111no—
538C2×#117—112no—
539C2×#117—111no—
540C2×#117—111no—
541C22×C4⋊C4—111no—
542C22×C4⋊C4—111no—
543C22×C42—111no—
544C22×C42—112no—
545C22×C42—111no—
546C22×C42—111no—
547#400—112no—
548#400—112no—
549#399—112no—
550#399C2×D1112yes—
551#398—112no—
552#398—112no—
553#397—112no—
554#397—112no—
555#397—112no—
556#397—112no—
557#397—112no—
558#397C2×D1112yes—
559#394—112no—
560#394—112no—
561#394—112no—
562#394—112no—
563#391—111no—
564#391—111no—
565#391—111no—
566#391—111no—
567#391—111no—
568#391C2×D1111yescharacteristic
569#390—111no—
570#390—111no—
571#390—111no—
572#390—111no—
573#390C2×D1111yescharacteristic
574#390C2×D1111yescharacteristic
575#389—111no—
576#389—111no—
577#389—111no—
578#389C2×D1111yescharacteristic
579#388—112no—
580#388—112no—
581#388C2×D1112yes—
582#388C2×D1112yes—
583#387—112no—
584#387—112no—
585#387—112no—
586#387—112no—
587#386—112no—
588#386—112no—
589#386—112no—
590#386—112no—
591#386—112no—
592#386—112no—
593#386—112no—
594#386—112no—
595#385—112no—
596#385—112no—
597#385—112no—
598#385—112no—
599#381—112no—
600#381—112no—
601C4×C4⋊C4—111no—
602C4×C4⋊C4—112no—
603C4×C4⋊C4—111no—
604C4×C4⋊C4—111no—
605C4×C4⋊C4—111no—
606C4×C4⋊C4—111no—
607C4×C4⋊C4—111no—
608C4×C4⋊C4—112no—
609C4×C4⋊C4—111no—
610C4×C4⋊C4C2×D1111yescharacteristic
611C4×C22⋊C4—112no—
612C4×C22⋊C4—112no—
613C4×C22⋊C4—112no—
614C4×C22⋊C4—112no—
615C4×C22⋊C4—112no—
616C4×C22⋊C4—112no—
617C2×#95—111no—
618C2×#95—111no—
619C22×C11—42no—
620C22×C11—42no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11C23×D411yescharacteristic
627C22×C11C22×#4111yescharacteristic
628C22×C11C22×#4111yescharacteristic
629C22×C11C22×#4111yescharacteristic
630C22×C11C22×#4111yescharacteristic
631C22×C11#58511yescharacteristic
632C22×C11#58511yescharacteristic
633C2×D11—22no—
634C2×D11—22no—
635C2×D11—22no—
636C2×D11—22no—
637C2×D11—22no—
638C2×D11—22no—
639C2×D11—24no—
640C2×D11—24no—
641C2×D11—24no—
642C2×D11—42no—
643C2×D11—42no—
644C2×D11—42no—
645C2×D11—42no—
646C2×D11C2×#12314yes—
647C4×C11—24no—
648C4×C11—22no—
649C4×C11—22no—
650C4×C11—41no—
651C4×C11—41no—
652C4×C11—41no—
653C4×C11—42no—
654C4×C11—41no—
655C4×C11—42no—
656C4×C11C2×#12314yes—
657Dic11—22no—
658Dic11—22no—
659Dic11—22no—
660Dic11—22no—
661Dic11—42no—
662Dic11—41no—
663Dic11—41no—
664Dic11—42no—
665Dic11—42no—
666Dic11C2×#12314yes—
667C2×#41—118no—
668C2×#41—224no—
669C2×#41—224no—
670C2×#41—224no—
671C2×#41—224no—
672C2×#41—224no—
673C22×Q8—111no—
674C22×Q8C22×D1111yescharacteristic
675C22×D4—112no—
676C22×D4—112no—
677C22×D4—112no—
678C22×D4—112no—
679C22×D4—111no—
680C22×D4C22×D1111yescharacteristic
681C23×C4—111no—
682C23×C4—112no—
683C23×C4—112no—
684C23×C4—111no—
685C23×C4—111no—
686C23×C4—111no—
687C23×C4—111no—
688C23×C4—111no—
689C23×C4—112no—
690C23×C4—112no—
691C23×C4—111no—
692C4⋊Q8—224no—
693#127—224no—
694#124—24no—
695#124—224no—
696#123—228no—
697#123—228no—
698#121—228no—
699#121—228no—
700C4×Q8—24no—
701C4×Q8—224no—
702C4×D4—228no—
703C4×D4—224no—
704C4×D4—228no—
705C4×D4—228no—
706C4×D4—228no—
707C4×D4—224no—
708#117—224no—
709#117—228no—
710#117—224no—
711C2×C4⋊C4—111no—
712C2×C4⋊C4—111no—
713C2×C4⋊C4—111no—
714C2×C4⋊C4—111no—
715C2×C4⋊C4—111no—
716C2×C4⋊C4—111no—
717C2×C4⋊C4—111no—
718C2×C4⋊C4—112no—
719C2×C4⋊C4—111no—
720C2×C4⋊C4—112no—
721C2×C4⋊C4—112no—
722C2×C4⋊C4—112no—
723C2×C4⋊C4—112no—
724C2×C4⋊C4—112no—
725C2×C4⋊C4—224no—
726C2×C4⋊C4—224no—
727C2×C4⋊C4C22×D1111yescharacteristic
728C2×C4⋊C4C22×D1111yescharacteristic
729C2×C4⋊C4C22×D1111yescharacteristic
730C2×C4⋊C4C22×D1112yes—
731C2×C4⋊C4C22×D1111yescharacteristic
732C2×C4⋊C4C22×D1112yes—
733C2×C22⋊C4—112no—
734C2×C22⋊C4—112no—
735C2×C22⋊C4—112no—
736C2×C22⋊C4—112no—
737C2×C22⋊C4—112no—
738C2×C22⋊C4—112no—
739C2×C22⋊C4—112no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—112no—
744C2×C22⋊C4—112no—
745C2×C22⋊C4—112no—
746C2×C22⋊C4—112no—
747C2×C22⋊C4C22×D1112yes—
748C2×C22⋊C4C22×D1112yes—
749C2×C22⋊C4C22×D1112yes—
750C2×C22⋊C4C22×D1112yes—
751C2×C22⋊C4C22×D1112yes—
752C2×C22⋊C4C22×D1112yes—
753C2×C42—111no—
754C2×C42—112no—
755C2×C42—112no—
756C2×C42—111no—
757C2×C42—111no—
758C2×C42—111no—
759C2×C42—112no—
760C2×C42—111no—
761C2×C42—111no—
762C2×C42—111no—
763C2×C42—111no—
764C2×C42—111no—
765C2×C42—224no—
766C2×C42—228no—
767C2×C42—224no—
768C2×C42—224no—
769C2×C42C22×D1111yescharacteristic
770C2×C42C22×D1112yes—
771C2×C42C22×D1111yescharacteristic
772C2×C42C22×D1111yescharacteristic
773#95—111no—
774#95—111no—
775#95—111no—
776#95—111no—
777#95—111no—
778#95—111no—
779#95—112no—
780#95—112no—
781#95—112no—
782#95—112no—
783#95—112no—
784#95—112no—
785#95—112no—
786#95—112no—
787#95—112no—
788#95—112no—
789#95—112no—
790#95—112no—
791#95—112no—
792#95C22×D1111yescharacteristic
793#95C22×D1111yescharacteristic
794#95C22×D1112yes—
795#95C22×D1112yes—
796#95C22×D1112yes—
797C2×C11—82no—
798C2×C11C22×#12311yescharacteristic
799C2×C11#344411yescharacteristic
800C2×C11#345511yescharacteristic
801C2×C11D4×#4111yescharacteristic
802C2×C11D4×#4111yescharacteristic
803C2×C11#348011yescharacteristic
804C2×C11#348011yescharacteristic
805D11—24no—
806D11—44no—
807C24—111no—
808C24—112no—
809C24C23×D1112yes—
810#41—2232no—
811#41—4416no—
812C2×Q8—22no—
813C2×Q8—22no—
814C2×Q8—222no—
815C2×Q8—222no—
816C2×Q8—222no—
817C2×Q8D4×D1114yes—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—118no—
822C2×D4—114no—
823C2×D4—224no—
824C2×D4—224no—
825C2×D4—224no—
826C2×D4—224no—
827C2×D4—224no—
828C2×D4—224no—
829C2×D4—224no—
830C2×D4—224no—
831C2×D4—224no—
832C2×D4—222no—
833C2×D4—222no—
834C2×D4—442no—
835C2×D4—442no—
836C22×C4—111no—
837C22×C4—114no—
838C22×C4—114no—
839C22×C4—114no—
840C22×C4—111no—
841C22×C4—111no—
842C22×C4—111no—
843C22×C4—111no—
844C22×C4—118no—
845C22×C4—111no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—111no—
850C22×C4—222no—
851C22×C4—224no—
852C22×C4—224no—
853C22×C4—222no—
854C22×C4—222no—
855C22×C4—222no—
856C22×C4—224no—
857C22×C4—222no—
858C22×C4—222no—
859C22×C4—224no—
860C22×C4—222no—
861C22×C4—224no—
862C22×C4—222no—
863C22×C4—222no—
864C22×C4—222no—
865C22×C4—224no—
866C22×C4—224no—
867C22×C4—224no—
868C22×C4—222no—
869C22×C4—222no—
870C22×C4—224no—
871C22×C4—441no—
872C22×C4—442no—
873C22×C4—441no—
874C22×C4—441no—
875C22×C4—442no—
876C22×C4—441no—
877C22×C4—441no—
878C22×C4—441no—
879C22×C4C23×D1111yescharacteristic
880C22×C4C23×D1112yes—
881C22×C4C23×D1111yescharacteristic
882C22×C4C23×D1112yes—
883C22×C4C23×D1111yescharacteristic
884C22×C4C23×D1111yescharacteristic
885C22×C4C23×D1112yes—
886C22×C4C23×D1111yescharacteristic
887C22×C4C23×D1111yescharacteristic
888C22×C4C23×D1111yescharacteristic
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—42no—
895C4⋊C4—114no—
896C4⋊C4—114no—
897C4⋊C4—222no—
898C4⋊C4—222no—
899C4⋊C4—222no—
900C4⋊C4—222no—
901C4⋊C4—224no—
902C4⋊C4—224no—
903C4⋊C4—224no—
904C4⋊C4—222no—
905C4⋊C4—224no—
906C4⋊C4—224no—
907C4⋊C4—222no—
908C4⋊C4—442no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—224no—
916C22⋊C4—224no—
917C22⋊C4—224no—
918C22⋊C4—224no—
919C22⋊C4—224no—
920C22⋊C4—224no—
921C22⋊C4—224no—
922C22⋊C4—224no—
923C22⋊C4—224no—
924C22⋊C4—224no—
925C22⋊C4—442no—
926C22⋊C4—442no—
927C22⋊C4—442no—
928C22⋊C4—442no—
929C42—24no—
930C42—22no—
931C42—22no—
932C42—22no—
933C42—222no—
934C42—222no—
935C42—224no—
936C42—222no—
937C42—222no—
938C42—222no—
939C42—222no—
940C42—224no—
941C42—224no—
942C42—222no—
943C42—222no—
944C42—222no—
945C11#3474411yescharacteristic, complemented, Sylow
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—112no—
954C23—112no—
955C23—112no—
956C23—114no—
957C23—221no—
958C23—221no—
959C23—221no—
960C23—221no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23C24×D1111yescharacteristic
968Q8—28no—
969Q8—444no—
970D4—44no—
971D4—2216no—
972D4—228no—
973D4—448no—
974D4—448no—
975D4—448no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—112no—
1001C2×C4—112no—
1002C2×C4—112no—
1003C2×C4—1116no—
1004C2×C4—112no—
1005C2×C4—112no—
1006C2×C4—112no—
1007C2×C4—112no—
1008C2×C4—2216no—
1009C2×C4—228no—
1010C2×C4—221no—
1011C2×C4—221no—
1012C2×C4—221no—
1013C2×C4—221no—
1014C2×C4—221no—
1015C2×C4—221no—
1016C2×C4—221no—
1017C2×C4—221no—
1018C2×C4—222no—
1019C2×C4—221no—
1020C2×C4—222no—
1021C2×C4—221no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—221no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—221no—
1029C2×C4—222no—
1030C2×C4—221no—
1031C2×C4—221no—
1032C2×C4—222no—
1033C2×C4—444no—
1034C2×C4—448no—
1035C2×C4—444no—
1036C2×C4—444no—
1037C2×C4—448no—
1038C2×C4—444no—
1039C2×C4—444no—
1040C2×C4—448no—
1041C2×C4C2×D4×D1114yes—
1042C2×C4C2×D4×D1112yes—
1043C2×C4#41×D1112yes—
1044C2×C4#41×D1112yes—
1045C2×C4#41×D1112yes—
1046C2×C4#41×D1112yes—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—114no—
1055C22—222no—
1056C22—222no—
1057C22—222no—
1058C22—222no—
1059C22—222no—
1060C22—222no—
1061C22—224no—
1062C22—224no—
1063C22—224no—
1064C22—442no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22C22×D4×D1111yescharacteristic
1069C22C2×#41×D1111yescharacteristic
1070C22C2×#41×D1111yescharacteristic
1071C22C2×#41×D1111yescharacteristic
1072C22C2×#41×D1111yescharacteristic
1073C22#1062345511yescharacteristic
1074C22#1062345711yescharacteristic
1075C4—22no—
1076C4—24no—
1077C4—22no—
1078C4—42no—
1079C4—41no—
1080C4—41no—
1081C4—41no—
1082C4—42no—
1083C4—41no—
1084C4—114no—
1085C4—222no—
1086C4—222no—
1087C4—222no—
1088C4—222no—
1089C4—442no—
1090C4—441no—
1091C4—442no—
1092C4—442no—
1093C4—441no—
1094C4D11×#12314yes—
1095C2—82no—
1096C2—224no—
1097C2—444no—
1098C2C2×D11×#12311yescharacteristic
1099C2#1308191011yescharacteristic
1100C2#1308200311yescharacteristic
1101C2#1308210511yescharacteristic
1102C2#1308210611yescharacteristic
1103C2#1308220811yescharacteristic
1104C2#1308221211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2448C2
prime radicalC2×#10623199C2
hypercenter#2448D11
hypocenterC11#34744
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2448

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×#4343C2semidirect
3. #13072410C2semidirect
4. #13072405C2semidirect
5. #13072403C2semidirect
6. #13072390C2semidirect
7. #13072386C2semidirect
8. #13072384C2semidirect
9. #13072382C2semidirect
10. #13072373C2semidirect
11. #13072369C2semidirect
12. #13072358C2semidirect
13. #13072354C2semidirect
14. #13071881C2semidirect
15. #13071878C2semidirect
16. #13071143C2semidirect
17. #13071143C2semidirect
18. #13071105C2semidirect
19. #13071103C2semidirect
20. #13071103C2semidirect
21. #13071097C2semidirect
22. C4×C4⋊C4×D11C2semidirect
23. C11×#2448C2semidirect
373. C4⋊Dic11#41semidirect
381. Dic11⋊C4#41semidirect
397. #2448D11semidirect
516. C4×D11#123semidirect
945. C11#34744semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106231992
C2×C4×#43432
#130724102
#130724052
#130724032
#130723902
#130723862
#130723842
#130723822
#130723732
#130723692
#130723582
#130723542
#130718812
#130718782
#130711432
#130711052
#130711032
#130710972
C4×C4⋊C4×D112
C11×#24482
#3474411